Orthogonal Frequency Division Multiplexing (OFDM) is the dominant multiplexing and modulation technique used in wireless communications. OFDM transmits multiple data streams by assigning each of them uniquely to one or more of a large number of sub-carriers where each sub-carrier operates at a unique carrier frequency (tone). The adjacent sub-carrier frequencies or tones have a fixed frequency difference between them. The data is carried in each sub-carrier by modulating its amplitude or phase, or both. For instance, phase shift keying (PSK) can be used to code the data into the phase of the subcarrier. An alternative form of modulation commonly used with OFDM is Quadrature Amplitude Modulation (QAM).
Quadrature Amplitude Modulation (QAM) codes a data signal comprising a series of symbols into two signals, respectively called the I-signal and the Q-signal. The I-signal and the Q-signal then modulate the amplitudes of two respective carriers that have the same frequency but whose phases differ by 90 degrees. For example, the I-signal carrier is presented by cos(2πft) and the Q-signal carrier is represented by sin(2πft). In the simplest form each symbol is coded either “1” or “0” (using one bit for each I-signal symbol without using the Q-signal). However it is more common for each symbol to be coded with more than two values; for instance 16QAM codes each symbol into one of sixteen values (using four bits). This is commonly represented by constellation diagram that uses the real axis I and imaginary axis Q to represent amplitude and phase; see FIG. 1.
In FIG. 1 the datum (0,0,0,0) is shown top left, and the datum (1,1,1,1) is shown bottom right. These corner signals have maximum amplitude, and they have the peak power as shown at 10. Whereas the average power is shown at circle 12. As a result this constellation has a peak-to-average power ratio (PAPR) equal to 2.5527 dB, which is the minimum PAPR for single-carrier (SC) modulation.
However, when OFDM is used to transmit many 16QAM symbols simultaneously it uses many subcarriers, for example 352 subcarriers, and in consequence the PAPR is increased. Without any PAPR reduction, the PAPR of a standard OFDM signal using 352 subcarriers and 16QAM could reach 28.0181 dB. In consequence, to completely eliminate distortion, the transmitter will occasionally be required to transmit 38.0181 dBm even though the required average power is only 10 dBm.
In this example of OFDM with 16QAM, out of the 512 tones only 352 tones are used for data and pilot 20, and 160 tones are unused. Normally 157 of the unused tones are located at the two ends of the channel bandwidth 22, and 3 of the unused tones are located around the centre of the channel bandwidth 24; see FIG. 2.
In conclusion, while OFDM has many advantages, it does generally suffer from a high peak-to-average power ratio (PAPR) compared to the conventional single carrier (SC) modulation. The peak power of an OFDM signal can be much higher than its average power; in other words, an OFDM signal can have a very large dynamic range. When a signal with high PAPR is used for communication, it will have the following three disadvantages:
1. To meet the peak power requirement, the transmitter (TX) maximum output power has to be high, resulting in high power and high cost.
2. All circuits, and especially the power amplifiers (PA), exhibit more non-linearity to a signal with higher PAPR. The nonlinearity causes the signal to spill into adjacent channels, resulting in Adjacent Channel Interference (ACI). In addition, the nonlinearity causes in-band distortion, resulting in performance loss or higher error rate.3. A higher PAPR signal requires more bits per sample for digital processing. For example, the number of bits in the transmitter's digital-to-analogue converter (DAC) has to be increased to accommodate the larger dynamic range. This is another factor for power and cost increase.
Overall, high PAPR implies large size, high cost, high power and low performance.
Intuitively the PAPR problem can be tackled by improving the analogue circuitry to achieve greater linearity, higher power operation and wider dynamic range. However in practice, this approach has proved expensive and unreliable, since it is difficult to accurately control the parameters of an analogue circuit.